Question

Find the value of a and b :- ✓3-1/✓3+1 = a +b✓3

Answer 1

$\textbf{Solution:}$

$\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} = a + b \sqrt{3} \\ \\ \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} \\ \\ \frac{( \sqrt{3 } - 1) {}^{2} }{( \sqrt{3} ) {}^{2} - (1) {}^{2} } \\ \\ \frac{3 - 2 \sqrt{3} + 1 }{3 - 1} \\ \\ \frac{4 - 2 \sqrt{3} }{2} \\ \\ \frac{2(2 - \sqrt{3} )}{2} = 2 - \sqrt{3}$

Therefore, the value of a = 2 and b = -1

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